What is expand (a+b)/(|(a+b)^2-1|) ?

The solution to expand (a+b)/(|(a+b)^2-1|) is a/(|a^2+2ab+b^2-1|)+b/(|a^2+2ab+b^2-1|)

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expand (a+b)/(|(a+b)^2-1|)

expand

\frac{a + b}{( a + b ) ^{2} - 1}

\frac{a}{∣ a ^{2} + 2 ab + b ^{2} - 1 ∣} + \frac{b}{∣ a ^{2} + 2 ab + b ^{2} - 1 ∣}

Solution steps

\frac{a + b}{( a + b ) ^{2} - 1}

Expand

(a + b)^{2} - 1 : a^{2} + 2 ab + b^{2} - 1

= \frac{a + b}{∣ a ^{2} + 2 ab + b ^{2} - 1 ∣}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{a + b}{∣ a ^{2} + 2 ab + b ^{2} - 1 ∣} = \frac{a}{∣ a ^{2} + 2 ab + b ^{2} - 1 ∣} + \frac{b}{∣ a ^{2} + 2 ab + b ^{2} - 1 ∣}

= \frac{a}{∣ a ^{2} + 2 ab + b ^{2} - 1 ∣} + \frac{b}{∣ a ^{2} + 2 ab + b ^{2} - 1 ∣}

\frac{1}{s ^{2} ( s ^{2} + 2 s + 2 ) - s}

\frac{- 3 s - 5}{2 ( s + 1 ) ( s + 4 ) ( s + 3 )}

\frac{3}{x + 5} + \frac{7}{x - 2}

18 ((x - 1)^{3} (x - 3)^{11})

(6 x y^{3} + cos (y)) d x + (3 k x^{2} y^{2} - 3 y^{2}) d y

What is expand (a+b)/(|(a+b)^2-1|) ?
The solution to expand (a+b)/(|(a+b)^2-1|) is a/(|a^2+2ab+b^2-1|)+b/(|a^2+2ab+b^2-1|)